THEMATIC SEMESTER

Overview

In 1979, Deligne formulated a far-reaching body of conjectures relating special values of L-functions arising in arithmetic geometry (more precisely, pieces of the cohomology of algebraic variety cut out by correspondences, the so-called motives of Grothendieck) to associated periods — ostensibly transcendental quantities which encode the difference between natural rational structures on DeRham and Betti cohomology. These conjectures, which applied to integer points that are critical in the sense of Deligne, were later extended by Bloch and Beilinson to non-critical points (building on the earlier insights of Borel in the case of the Riemann zeta-function and Dirichlet L-functions) expressing these special values in terms of certain regulators on Higher Chow groups and K-groups that are naturally associated to the relevant motive. In the last decade, David Boyd discovered a number of tantalising and appealingly concrete identities relating Mahler Measures to similar special values of L-functions, which were then extended by a host of other mathematicians. One goal of this workshop will be to integrate these identities more solidly within the overarching but largely conjectural framework governing the behaviour of special values of L-functions.